FIN401-Quantitative review - QUANTITATIVE REVIEW Time Value...

QUANTITATIVE REVIEWTime Value of Money:Evaluating financial transactions requires valuing uncertain future cash flows. Determinants of future value: Present valueCompounding periodsInterest rateCOMPOUND (FUTURE) VALUE:FV = Pv(1+i)^n Frequency of compounding:When interest is compounded more frequently than on an annual basis, adjust the interest rateand the compounding periods, accordingly.Continuous compounding: One can compound multiple periods per year (semiannually, quarterly, monthly, daily, hourly, etc.). The limiting case would be to compound every infinitesimal instant, which is commonly called continuous compounding. The compound factor uses the exponential function, e, the inverse of the natural logarithm. Continuous compounding = PV[e^(i)(n)]Example: Suppose you invest $5,000 in an account that earns 10% interest. How much more would you have after 20 years if interest is compounded continuously instead of compounded semi-annually?Semiannually: $35199.94Continuously: $36945.28Difference:$1745.34PRESENT VALUE:Translating a value back in time (discounting) to determine what a future amount or cash flow is worth today. FV FV[ 1/(1+i)^n]PV = (1+i)^n or From the formula for the present value we know that:oas the number of discount periods, n, becomes smaller, the discount factor becomes smaller and the present value becomes larger, andoas the interest rate per period, i, becomes smaller, the discount factor becomes smaller and the present value becomes larger.

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